中国科学院数学与系统科学研究院期刊网

2026年, 第39卷, 第5期 刊出日期:2026-09-17
  

  • 全选
    |
  • SUN Yao, ZHENG Dabin
    系统科学与复杂性(英文). 2026, 39(5): 1879-1880. https://doi.org/10.1007/s11424-026-6003-0
    摘要 ( ) PDF全文 ( )   可视化   收藏
  • TANG Xiaoxian, WANG Yihan, ZHANG Jiandong
    系统科学与复杂性(英文). 2026, 39(5): 1881-1900. https://doi.org/10.1007/s11424-026-5441-z
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Zero-one biochemical reaction networks are widely recognized for their importance in analyzing signal transduction and cellular decision-making processes. Degenerate networks reveal non-standard behaviors and mark the boundary where classical methods fail. Their analysis is key to understanding exceptional dynamical phenomena in biochemical systems. Therefore, the authors focus on investigating the degeneracy of zero-one reaction networks. It is known that one-dimensional zero-one networks cannot degenerate. In this work, the authors identify all degenerate two-dimensional zero-one reaction networks with up to three species by an efficient algorithm. By analyzing the structure of these networks, the authors arrive at the following conclusion: If a two-dimensional zero-one reaction network with three species is degenerate, then its steady-state system is equivalent to a binomial system.
  • GAO Yueming, ZHU Chungang
    系统科学与复杂性(英文). 2026, 39(5): 1901-1925. https://doi.org/10.1007/s11424-026-5379-1
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In Isogeometric Analysis (IGA), constructing high-quality analysis-suitable computational domain parameterizations is a crucial issue. In recent years, learning-based parameterization methods have attracted attention with the development of machine learning and deep learning. This paper proposes a novel learning-based domain parameterization method for IGA. The proposed method employs Physics-Informed Neural Networks (PINNs) to solve Partial Differential Equations (PDEs) associated with parameterizations. To achieve high-quality parameterizations, the loss function incorporates both angular distortion and area distortion during the construction process. Furthermore, the authors introduce a penalty function-based Jacobian regularization strategy that enhances network training stability and ensures the generation of analysis-suitable parameterizations. After training the network, the authors use tensor-product B-splines to fit the results and construct the parameterizations. Numerical examples demonstrate that the proposed method achieves superior orthogonality and uniformity compared to existing deep learning-based parameterization approaches for complex planar computational domains. Additionally, the proposed method can be extended to volume parameterizations for 3D computational domains.
  • XIA Peng, LEI Na, LIU Zixia
    系统科学与复杂性(英文). 2026, 39(5): 1926-1949. https://doi.org/10.1007/s11424-026-5407-1
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Floater-Hormann barycentric rational interpolation is a family of interpolation methods with high approximation precision. Based on Floater-Hormann barycentric rational interpolation, researches have provided algorithms for solving ODEs. Since barycentric rational interpolation function has one uniform expression $r(x)$ on the entire interval, when there are local changes in interpolation data, $r(x)$ changes globally. When solving ODEs, the coefficient matrix of linear equations obtained based on $r(x)$ is dense, which brings complexities for solving equations. To overcome these problems, a weighted piecewise barycentric rational interpolation method is established in this work. Regarding the interpolation case, when there are local changes in data, the interpolation function obtained by the proposed method only changes locally. When solving two-point boundary value problems based on weighted piecewise barycentric rational interpolation method, number of non-zero elements in the obtained coefficient matrix reduces with the increase of ``pieces''. Especially, under specific conditions for dividing pieces, the coefficient matrix reduces to a 3-diagonal matrix. Experiments show that, this kind of weighted piecewise barycentric rational interpolation method has some advantages for both interpolation and solving two-point boundary value problems.
  • HE Xin, YANG Li, JIA Lijie, HUANG Yi, WANG Weiming
    系统科学与复杂性(英文). 2026, 39(5): 1950-1967. https://doi.org/10.1007/s11424-026-5391-5
    摘要 ( )   可视化   收藏
    Topology optimization offers lightweight and high-performance solutions for structural design. With the rapid advancement of neural networks, topology optimization methods leveraging neural architectures have gained increasing attention. Among these methods, positional encoding is crucial for enabling neural networks to capture high-frequency geometry features, making its integration into neural network-based optimization methods a promising direction for exploration. This paper focuses on positional encoding by introducing a spline-based positional encoding into the neural topology optimization framework, in which spatial coordinates are transformed using spline basis functions before being input into the neural network. The performance of different classic spline basis functions is comprehensively evaluated, including the Bézier spline, B-spline, and NURBS spline. Experimental results demonstrate that positional encoding based on quadratic B-spline basis functions yields the highest structural stiffness. To further validate the effectiveness of the proposed method, a comparative analysis is performed against Fourier and super-Gaussian positional encoding schemes. The results show that spline-based encoding outperforms both alternatives in terms of structural compliance in most cases. Moreover, the resulting topologies exhibit smooth boundaries, free from oscillations and superfluous geometric details.
  • YIN Zhedong, DONG Bo, YU Yan, GAO Chenyu
    系统科学与复杂性(英文). 2026, 39(5): 1968-1986. https://doi.org/10.1007/s11424-026-5445-8
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Polynomial multiparameter eigenvalue problems (PMEPs) arise in various applications, such as aeroelastic flutter problems, delay differential equations, and ARMA models. The existing methods for solving this problem linearize them as multiparameter eigenvalue problems (MEPs). However, this method is only applicable to specific problems. To the best of our knowledge, there is no method for solving the general PMEPs. This paper presents a homotopy continuation method to find all solutions to PMEPs. The convergence of the method is proved using techniques from algebraic geometry and numerical linear algebra. An acceleration technique for path tracking is also proposed, and numerical results show the effectiveness of the homotopy method.
  • HE Shitao, SHEN Liyong, YUAN Chunming, MA Hongyu
    系统科学与复杂性(英文). 2026, 39(5): 1987-2022. https://doi.org/10.1007/s11424-026-5381-7
    摘要 ( ) PDF全文 ( )   可视化   收藏
    The ACC/DEC method to schedule the feedrate is widely used in 3-axis CNC machining due to its simplicity and effectiveness. However, for most of the existing methods, the chord error is computed by an approximate way, which can not strictly control the chord error. In this paper, the feedrate scheduling for a NURBS toolpath is considered and it is transformed to construct an information matrix, with the help of which it can be found that the key issue of feedrate scheduling is to update the matrix by three kinds of basic operation. To control the chord error strictly, it is proven that the calculation of chord error can be transformed into finding the real roots of algebraic equations. Then, the feasibility of the feedrate can be guaranteed by adjusting the information matrix. To improve the efficiency of the machining, several optimal strategies are proposed. The simulation results show that the proposed method can strictly control the chord error with relatively shorter machining time compared with other ACC/DEC methods.
  • HE Lei, ZHAO Lina, YANG Hongwei, MENG Xiang, WANG Ruyue, ZHANG Guifang
    系统科学与复杂性(英文). 2026, 39(5): 2023-2048. https://doi.org/10.1007/s11424-026-5410-6
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Convolutional neural networks (CNNs) have been widely utilized in hyperspectral image (HSI) classification tasks, achieving remarkable performance. However, in existing HSI-CNN methods, the cubic information in HSI is often vectorized, which can compromise the geometric structure of the data. Meanwhile, how to break through the bottleneck of parameter redundancy and immense computation consumption is a hot topic in CNN-based methods. Inspired by these, a stand-alone tensor neural network (SATNN) is proposed, which uses tensor algebra to construct a deep learning framework to replace the convolutional, pooling, and fully connected layers typically found in CNNs. Feature extraction is carried out among the tensor contraction layer (TCOL), tensor pattern product layer (TMPL), tensor replacing the flatten operation, and the fully-connected layer (TRFFC), which can capture the geometric structure and multilinear structure of high-dimensional data. What is important, TCOL can reduce the parameters of LeNet-5 and the hybrid spectral convolution neural network (HybridSN) by 64.46% and 98.24% with little effect on precision. Experiment results on three commonly used hyperspectral imagery datasets demonstrate the effectiveness of HSI-SATNN, with its classification accuracy surpassing that of several CNN-based and tensor-based approaches.
  • MAO Chen, LIU Ping
    系统科学与复杂性(英文). 2026, 39(5): 2049-2071. https://doi.org/10.1007/s11424-026-5399-x
    摘要 ( ) PDF全文 ( )   可视化   收藏
    This paper presents a stochastic chemostat model driven by three independent Brownian motions. In addition to the direct disturbances caused by environmental noise on microorganisms and substrates (such as fluctuations in mortality rates and dilution rates), the feature of this paper is the introduction of randomness in the absorption or metabolic process of microorganisms for substrates, which reflects the interaction between substrates and microorganisms being modulated by common environmental noise and also describes the two-way stochastic coupling of substrate consumption and microbial growth. The authors focus on the dynamics of the system and successfully define the threshold λ that determines the existence and extinction of the population: When λ is positive, microorganisms will persist existence, and the authors prove the existence of unique stationary distribution of the system by constructing an auxiliary function; when λ is negative, microorganisms tend to extinction, and the substrate concentration distribution weakly converges to the probability measure π1*. Numerical simulation results are in complete agreement with theoretical analysis, and the authors illustrate how the intensity of noise affects the threshold λ through specific examples. The authors also verify the uniqueness of the stationary distribution by using kernel density estimation.
  • TAO Zheng, HU Zhi
    系统科学与复杂性(英文). 2026, 39(5): 2072-2095. https://doi.org/10.1007/s11424-026-5124-9
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Elliptic curves over finite fields have been extensively used to build public key cryptography (a.k.a. Elliptic Curve Cryptography (ECC)). The choice of elliptic curves significantly affects the security and performance of the relevant cryptosystem. At present, standardized curves in ECC are all defined over finite fields of characteristic 2 or large prime characteristic, while those of characteristic 3 have drawn little attention mainly due to their lower efficiency in implementation. In this work, the authors primarily study ordinary elliptic curves defined over the quadratic extension field of characteristic 3 equipped with the Frobenius endomorphism. All relevant operations of finite field and elliptic curves, implemented by the AVX2 instructions and 256-bit wide SIMD operands, are developed and optimized to ensure both efficient and constant-time execution. At the 128-bit security level, the proposed implementation is approximately 1.8 times faster than the previous work for scalar multiplication on ordinary curves of characteristic 3. To the best of our knowledge, this is the first scalar multiplication implementation on elliptic curves of characteristic 3 which outperforms those on standard curves such as NIST P-256 and SM2.
  • CHEN Guangdeng, ZHU Panming, PENG Xiao-Jie, HUANG Chao, LI Hongyi
    系统科学与复杂性(英文). 2026, 39(5): 2096-2118. https://doi.org/10.1007/s11424-026-5060-8
    摘要 ( ) PDF全文 ( )   可视化   收藏
    This article studies attack detection problems for the secure distributed state estimation of multi-sensor networks with intermittent observation. The Kalman consensus filter is equipped to develop the minimum mean square error estimation of the process. Due to the vulnerability of the communication network, an attack scenario is considered in which both the sensor-to-estimator channels and the estimator-to-estimator channels are attacked. The attackers would intercept and modify the measurement based on a linear attack strategy. Meanwhile, the false data are injected into the prior state estimates sent to other nodes. The $\chi^2$ detectors fail to identify the well-designed linear and false data injection attacks. To overcome this drawback, a watermarking-based attack detection strategy is proposed. The effectiveness of the proposed scheme for stealthy attacks is analyzed. Furthermore, the presence of intermittent observations prevents the residuals from reflecting false data injection attacks in estimator-to-estimator channels. This problem is effectively addressed by employing a stochastic detection strategy integrated with watermarking. Based on effective attack detection, malicious data can be mitigated using the Kalman consensus filter to avoid performance degradation. Finally, a numerical simulation validates the effectiveness of the proposed method.
  • WANG Xiaowen, LIU Shuai, XU Qianwen, SHAO Xinquan
    系统科学与复杂性(英文). 2026, 39(5): 2119-2145. https://doi.org/10.1007/s11424-026-4658-1
    摘要 ( ) PDF全文 ( )   可视化   收藏
    The operation of a microgrid (MG) system with multiple nodes not only needs to solve the optimization problem of economic dispatch but also has to consider the optimization goals of the safe and environmentally friendly operation. Therefore, the purpose of each node with renewable resources is to collaborate to achieve the optimization of multiple objectives. In this paper, the authors shall design a deep reinforcement learning (DRL) algorithm to perform the multi-objective optimization which can handle continuous action space and determine the specific output power of each device. Unlike the existing algorithms that learn policies with holistic reward signals, the proposed algorithm decomposes the reward into multiple parts and trains multiple critic networks for sub-objectives to get the Pareto optimal solutions. The proposal of single-actor multi-critic architecture not only can avoid task-specific local optimal policies but also does not need to set weight values. The effectiveness of the algorithm is verified by case studies on a modified IEEE-30 bus system and a modified IEEE-118 bus system. After training, the DRL agent can adapt to the high uncertainty of the photovoltaics and exploit the capacity of battery energy storage stations safely, which is more practical in a real system.
  • SUN Yawen, LI Hongdan, ZHANG Huanshui, LI Xun
    系统科学与复杂性(英文). 2026, 39(5): 2146-2163. https://doi.org/10.1007/s11424-026-5110-2
    摘要 ( ) PDF全文 ( )   可视化   收藏
    This paper investigates the decentralized linear quadratic control problem for systems with observation and multiplicative noise. The system is controlled by two controllers, where the available information for the second controller involves the first controller. Multiplicative noise and observation arise simultaneously in the system model, which differs from the existing literature. The inapplicability of the separation principle and the highly nonlinear characteristics of the observation-based controller optimization problem make the search for the optimal solution quite difficult. The explicit output feedback controllers are designed based on the linear estimator using the matrix maximum principle. An iterative algorithm is presented to compute the gain matrices, and a sufficient condition is given for the mean-square stability of the system. Finally, a vehicle platoon problem is tackled with the acquired theoretical results.
  • REN Hanjing, GUO Baozhu
    系统科学与复杂性(英文). 2026, 39(5): 2164-2187. https://doi.org/10.1007/s11424-025-5227-8
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper, the authors analyze the uniform exponential stability of a semi-discrete scheme for a coupled system derived from a one-dimensional wave equation, which is subject to boundary feedback with noncollocated observation. This system was previously studied in the paper (Guo B Z and Xu C Z, 2007), where the Riesz basis methodology was utilized. However, it is critical to acknowledge that the Riesz basis approach is inadequate for addressing the uniform exponential stability of discrete schemes. In contrast, the Lyapunov function offers a more straightforward alternative approach. Therefore, the authors first establish exponential stability by constructing a global Lyapunov function for the closed-loop system. Subsequently, employing the order reduction method, the authors derive the semi-discrete finite difference (FD) scheme of the system. Analogous to the demonstration for the continuous case, the authors construct discrete Lyapunov functions and utilize them to demonstrate that the discretized scheme exhibits uniformly exponential decay as the step size approaches zero.
  • FU Shihua, FENG Jun-e, YU Ling, NIE Xueying, PAN Ya-nan, ZHAO Xiaoyu
    系统科学与复杂性(英文). 2026, 39(5): 2188-2205. https://doi.org/10.1007/s11424-025-5077-4
    摘要 ( ) PDF全文 ( )   可视化   收藏
    This paper investigates the Pareto-Nash equilibria for multicriteria normal games and multicriteria networked evolutionary games (MCNEGs) using the semi-tensor product of matrices. Firstly, an easy-to-verify matrix criterion is provided to calculate the Pareto-Nash equilibria of multicriteria normal games. Secondly, an algorithm is established to convert the dynamics of an MCNEG into an algebraic form. Thirdly, based on the algebraic form, a necessary and sufficient condition is presented to verify whether a profile is a Pareto-Nash equilibrium, and the asymptotic stability of an MCNEG to the Pareto-Nash equilibrium set is studied. Finally, an illustrative example is given to demonstrate the correctness of the new results.
  • LIU Xiongding, LU Qiang, ZHAO Xiaodan, ZHANG Botao, WEI Wu
    系统科学与复杂性(英文). 2026, 39(5): 2206-2226. https://doi.org/10.1007/s11424-025-4593-6
    摘要 ( ) PDF全文 ( )   可视化   收藏
    This paper studies the consensus tracking control of networked stochastic leader-following multi-agent systems (MASs) with multiplicative and additive time-varying actuator failures under random communication topology switching. Considering the measurement noise generated by information transmission in networked systems, the stochastic MASs model with multiplicative noise is established. Meanwhile, the random time-varying loss of actuator effectiveness failure and bias faults are taken into account. Based on the neighbors' and leaders' state, the distributed adaptive fault-tolerant consensus tracking control protocols are proposed under the case of Markovian and semi-Markovian switching topology. Using stochastic system theory and Lyapunov theorem, sufficient conditions of the mean-square practical stability for leader-following consensus tracking are obtained. Results show that under the proposed distributed adaptive fault-tolerant control (DAFTC) protocols, the follower agents can track the leader under actuator constrains and random switching topology. Finally, the effectiveness of the mentioned control protocols are verified the numerical simulations.
  • CHEN Xudong, QIAN Chongjiao, YU Zhiyong, JIANG Haijun
    系统科学与复杂性(英文). 2026, 39(5): 2227-2247. https://doi.org/10.1007/s11424-026-4644-7
    摘要 ( ) PDF全文 ( )   可视化   收藏
    This paper addresses the prescribed-time bipartite output consensus problem for linear heterogeneous multi-agent systems under a directed signed graph. Firstly, an improved prescribed-time convergence lemma is developed through the introduction of an auxiliary function, facilitating relaxed constraints on relevant parameters. Secondly, a prescribed-time distributed observer is proposed for locally known leader states by leveraging cooperative and competitive interactions among agents. Furthermore, this paper designs both continuous and event-triggered control protocols, whereby some sufficient conditions for achieving prescribed-time bipartite output consensus are obtained by using the proposed convergence lemma. Finally, several numerical simulations are presented to verify the validity of our theoretical results.
  • XU Menghao, YU Zhou, SHAO Jun
    系统科学与复杂性(英文). 2026, 39(5): 2248-2270. https://doi.org/10.1007/s11424-026-4163-6
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper, the authors propose a directional regression based approach for ultrahigh dimensional sufficient variable screening with censored responses. The new method is designed in a model-free manner and thus can be adapted to various complex model structures. Under some commonly used assumptions, the authors show that the proposed method enjoys the sure screening property when the dimension $p$ diverges at an exponential rate of the sample size $n$. To improve the marginal screening method, the corresponding iterative screening algorithm and stability screening algorithm are further equipped. The authors demonstrate the effectiveness of the proposed method through simulation studies and a real data analysis.
  • ZHENG Chunxu, LI Jie, SUN Shaolong, SHAO Hui, WANG Shouyang
    系统科学与复杂性(英文). 2026, 39(5): 2271-2291. https://doi.org/10.1007/s11424-026-4456-9
    摘要 ( ) PDF全文 ( )   可视化   收藏
    With the development of the tourism industry, the associated carbon dioxide emissions have become considerable, significantly impacting global climate change. This study will compile relevant publications from various fields in recent years on sustainable tourism and climate change, and analyse the hot issues in this field based on the bidirectional relationship between the tourism industry and climate change. Firstly, based on the research framework of the bidirectional relationship between tourism and climate change, the impact of the tourism industry on climate change was measured from the perspective of tourist carbon footprint in four aspects. Simultaneously, the effects of climate change on the tourism industry were summarized. Subsequently, bibliometric methods are employed to analyse the literature in this field in recent years. Finally, combining qualitative and quantitative review results, the study presents feasible suggestions for future research directions, highlighting potential avenues for further investigation from both technical and policy perspectives.
  • HUANG Chuangxia, DENG Yanchen, YANG Xiaoguang, CAI Yaqian, ZHAO Xian
    系统科学与复杂性(英文). 2026, 39(5): 2292-2318. https://doi.org/10.1007/s11424-025-4338-6
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Using a sample of Chinese listed firms for the period 2006-2021, this paper constructs dynamic stock networks annually using symbolization and mutual information methods, and investigates the impact of stock network centrality on one-year-ahead stock price crash risk with the help of the bad news hoarding mechanism. The authors find robust evidence that firms with higher centrality are less likely to experience stock price crashes in the future. An examination of underlying mechanisms suggests that being at the center of the stock network enhances firms' investment efficiency and managers' cost of engaging in earnings management, thereby reducing the likelihood of such firms forming and hoarding bad news, and hence their crash risk. Further analysis reveals that the mitigating effect of network centrality on stock price crashes is more salient for firms with weaker external monitoring and less conservative accounting policies. Overall, this paper sheds light on a novel benefit of being at the center of the stock network, namely that central firms are less prone to crash risk, which provides practical insights for risk-management applications related to asset pricing and tail events. %Overall, this paper sheds light on the firm less prone to crash risk is a novel benefit of being at the center of the stock network, which provides practical insights for risk-management applications related to asset pricing and tail events.
  • LU Haibo, CHEN Zhuojian, CHEN Zimu
    系统科学与复杂性(英文). 2026, 39(5): 2319-2340. https://doi.org/10.1007/s11424-025-4280-7
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In econometric analysis, researchers often encounter vast datasets that greatly reduce model efficiency. In this paper, the authors develop a sequential shrinkage estimation method for use in distributed settings. Within this framework, one dataset is split into several blocks, and each block is regarded as a node. The sequential shrinkage estimation method is implemented on the data in each block until the stopping criteria are satisfied. These sequential procedures are then integrated to produce the final results using a weighted average, which provides approximate regression result estimates for the entire dataset. The proposed method can significantly reduce the required number of samples and perform parameter estimation and variable selection while satisfying the preset accuracy requirements. In addition, the statistical properties of the parameter estimates in the proposed approach are analyzed for use in a linear regression model. Finally, numerical studies on simulated and real datasets show that the proposed method performs well.
  • XU Yikai, CHENG Ming, CHEN Zhao
    系统科学与复杂性(英文). 2026, 39(5): 2341-2373. https://doi.org/10.1007/s11424-025-5235-8
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Data censoring is a common problem during the process of survival data collection. To maximize the usable information in dataset with censoring, Cox model has been proposed and becomes of a benchmark model in censoring data modelling. However, as data size grows, challenging raises on learning Cox model and its modern extensions. Existing algorithms for training Cox model facing the problems of insufficient sample pair usage and control sample unbalance. In this work, the authors introduce the batch recombination algorithm: A chain-based method that better uses sample pairs while keeping control sample balance. The authors show that, under mild conditions, parameter estimates from stochastic gradient descent using our recombinated batch are consistent. Confidence interval can also be established using asymptotic distribution. Extensive numerical experiment both on simulated data and real data, linear and neural network Cox model show efficiency and accuracy of the proposed method.
  • LI Ziyang, PAN Sheng, ZHANG Shuyi, ZHOU Yong
    系统科学与复杂性(英文). 2026, 39(5): 2374-2402. https://doi.org/10.1007/s11424-025-5112-5
    摘要 ( ) PDF全文 ( )   可视化   收藏
    For copula models with unknown marginal distributions and an unspecified Euclidean parameter, a natural way to get a rank-based semiparametrically efficient estimator for the Euclidean parameter is to solve the estimating equation constructed using the efficient score, with the unknown marginal distribution functions substituted by the empirical versions. However, the solution may lack a closed form and may only be approximate. At present, it is not known how a rank-based semiparametrically efficient estimator can be found for general copula models. By using a given arbitrary consistent rank-based estimator as the initial point, the authors propose a $K$-step estimator that is more efficient, where $K$ is related to the convergence rate of the initial point. The authors show that, under regularity conditions, the $K$-step estimator achieves the semiparametric efficiency bound for general copula models. Numerical calculation methods are also presented. Finally, the authors perform simulations to demonstrate the superiority of the proposed method.